Question

In Exercises 1–4, use the following listed arrival delay times (minutes) for American Airline flights from New York to Los Angeles. Negative values correspond to flights that arrived early. Also shown are the SPSS results for analysis of variance. Assume that we plan to use a 0.05 significance level to test the claim that the different flights have the same mean arrival delay time.

Flight 1	-32	-25	-26	-6	5	-15	-17	-36
Flight 19	-5	-32	-13	-9	-19	49	-30	-23
Flight 21	-23	28	103	-19	-5	-46	13	-3

ANOVA

a. What characteristic of the data above indicates that we should use one-way analysis of variance?

b. If the objective is to test the claim that the three flights have the same mean arrival delay time, why is the method referred to as analysis of variance?

Short answer

1. The fact that the factor, arrival delay time, is compared over three different categories (flight numbers) indicates the use of one-way analysis of variance.

2. As three different mean values for varied categories of a single factor are desired to be compared using the two components of variance, the method is referred to as analysis of variance.

Step-by-step solution

Given information

The arrival delay times for three flights are known.

The significance level is known to be 0.05.

The SPSS output for analysis of variance is known.

Condition to use one-way analysis of variance

One-way analysis of variance is used for comparing the mean of the data for one particular factor over different categories.

Identify the characteristic

a.

The arrival delay times of three flights areknown.

The independent variable of the study, referred to as the factor, is the arrival delay time. The variable is categorized into three categories; flights 1, 19, and 21. For comparison of the factors across three different categories, a one-way analysis of variance can be used.

Explain the method of analysis of variance

b.

The method to compare the mean values of the arrival delay time of three flights is referred to as analysis of variance because the following two components of variance are involvedin testing the claim:

• Sum of squares between the groups
• Sum of squares within the groups.

These are further used to compute the test statistic based on F-distribution.